Sure, let's work step-by-step through the relationships given in your question to find the values of [tex]\(\omega\)[/tex] and [tex]\(a\)[/tex].
### Given:
1. [tex]\(\omega = x + 4\)[/tex]
2. [tex]\(1 + a = 5x + 2\)[/tex]
### Solve for [tex]\(\omega\)[/tex]:
To find [tex]\(\omega\)[/tex], let's assume [tex]\(x = 2\)[/tex] (as an example).
Substitute [tex]\(x\)[/tex] into the equation for [tex]\(\omega\)[/tex]:
[tex]\[ \omega = x + 4 \][/tex]
[tex]\[ \omega = 2 + 4 \][/tex]
[tex]\[ \omega = 6 \][/tex]
### Solve for [tex]\(a\)[/tex]:
We now use the equation [tex]\(1 + a = 5x + 2\)[/tex]. Substituting [tex]\(x = 2\)[/tex]:
[tex]\[ 1 + a = 5(2) + 2 \][/tex]
[tex]\[ 1 + a = 10 + 2 \][/tex]
[tex]\[ 1 + a = 12 \][/tex]
To isolate [tex]\(a\)[/tex], subtract 1 from both sides:
[tex]\[ a = 12 - 1 \][/tex]
[tex]\[ a = 11 \][/tex]
### Conclusion:
After completing the calculations step-by-step, we find the solutions to be:
- [tex]\(\omega = 6\)[/tex]
- [tex]\(a = 11\)[/tex]
So, the values of [tex]\(\omega\)[/tex] and [tex]\(a\)[/tex] are [tex]\(6\)[/tex] and [tex]\(11\)[/tex] respectively.
